Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
484 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #23757327 | C2 | semidirect |
| 3. #23757323 | C2 | semidirect |
| 4. #23757296 | C2 | semidirect |
| 6. M16×Dic157 | C2 | semidirect |
| 17. #19097700 | C22 | semidirect |
| 19. #19097681 | C22 | semidirect |
| 20. C8×Dic157 | C22 | semidirect |
| 56. C2×Dic157 | M16 | semidirect |
| 92. C157 | #2920 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic157 | 2 |
| #23757327 | 2 |
| #23757323 | 2 |
| #23757296 | 2 |
| #23757237 | 2 |
| M16×Dic157 | 2 |
| #407×C157 | 2 |
| #2920 | 157 |